Distance Measure for Fermatean Neutrosophic Sets: A  Comparative Framework for Qualitative Evaluation

S. Bhuvaneshwari; C. Antony Crispin Sweety; Broumi Said

Authors

S. Bhuvaneshwari Avinashilingam Institute for Home Science and Higher Education for Women. Coimbatore. Tamil Nadu. India;
C. Antony Crispin Sweety Avinashilingam Institute for Home Science and Higher Education for Women. Coimbatore. Tamil Nadu. India;
Broumi Said Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II. Casablanca. Morocco;

Keywords:

Fermatean Neutrosophic set; Euclidean Distance (ED), Normalized Euclidean Distance (N-ED), Hamming Distance (HD), Normalized Hamming Distance (N-HD), Sine Metric Single Valued Neutrosophic Distance Measure (SMSVNDM), Tangent Matric Fermatean Neutrosophic Distance Measure (TMFNDM).

Abstract

This work introduces a novel distance measure specifically designed for Fermatean
Neutrosophic sets (FNS), extending upon existing measures such as the intuitionistic fuzzy distance
and single-valued Neutrosophy distance measures. The study proposes a Hypothetical Framework
for Fermatean Neutrosophic Sets to evaluate minimum distances and compares six different
distance measures. These measures are applied within the contexts of both Fermatean Neutrosophic
Sets and Neutrosophic Sets. The primary objective is to identify the shortest distance, enabling
precise and appropriate decision-making. The study highlights the importance of false membership
in FNS, which alters the ranking of FNS and establishes the Fermatean Neutrosophic set as a more
accurate tool for evaluation in specific cases.

DOI: 10.5281/zenodo.14707614